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A limiting absorption principle for scattering problems with unbounded obstacles

✍ Scribed by Anne-Sophie Bonnet-Bendhia; Axel Tillequin

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 195 KB
Volume: 24
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.259

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✦ Synopsis

Abstract

A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two‐dimensional Helmholtz case. This method leads by variational means to an integro‐differential formulation whose unknown is the trace of the field on an unbounded one‐dimensional interface. The well‐posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result—based upon some properties of a singular integral operator similar to the Hilbert transform—the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd.

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In this series of papers we prove the limiting absorption principle over a given interval for a class of Hamiltonians which contains the original one of von Neumann and Wigner. More specifically, the Hamiltonians are of the form < < < < ␤ Ž . Ž . y⌬ q c sin b x r x q V x , where 2r3 -␤ F 1, V x is a